Non-linear free vibration of isotropic plates with internal resonance

Ribeiro, Pedro; Petyt, M.

doi:10.1016/s0020-7462(99)00013-x

Cited by 94 publications

(55 citation statements)

References 14 publications

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“…However, many vibrating systems are subject to non-linear behaviours, such as loudspeakers [1], musical instruments [2] and vibrating plates [3]. Even wave propagation in air is not completely linear [4].…”

Section: Introductionmentioning

confidence: 99%

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Identification of cascade of Hammerstein models for the description of nonlinearities in vibrating devices

Rébillat

Hennequin

Corteel³

et al. 2011

Journal of Sound and Vibration

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In a number of vibration applications, systems under study are slightly non-linear. It is thus of great importance to have a way to model and to measure these non-linearities in the frequency range of use. Cascade of Hammerstein models conveniently allows one to describe a large class of non-linearities. A simple method based on a phase property of exponential sine sweeps is proposed to identify the structural elements of such a model from only one measured response of the system. Mathematical foundations and practical implementation of the method are discussed. The method is afterwards validated on simulated and real systems. Vibrating devices such as acoustical transducers are well approximated by cascade of Hammerstein models. The harmonic distortion generated by those transducers can be predicted by the model over the entire audio frequency range for any desired input amplitude. Agreement with more time consuming classical distortion measurement methods was found to be good.

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Section: Introductionmentioning

confidence: 99%

“…In panel-based loudspeakers, large amplitude displacements occur in the plate near the exciter position. In this case the propagation of flexural waves [3] and the strain/stress relation of the material which compose the plate [19] can be non-linear.…”

Section: Introductionmentioning

confidence: 99%

Identification of cascade of Hammerstein models for the description of nonlinearities in vibrating devices

Rébillat

Hennequin

Corteel³

et al. 2011

Journal of Sound and Vibration

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“…Asymmetric linear vibrations of circular plates of linearly varying thickness have also been considered recently in references [16,17]. Finally, recent development in computer simulations leads to numerical studies, which generally use a finite element method combined with the harmonic balance method, see for example references [18,19].…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Non-Linear Forced Vibrations of Free-Edge Circular Plates. Part 1: Theory

Touzé¹,

Thomas²,

Chaigne³

2002

Journal of Sound and Vibration

100

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In this article, a detailed study of the forced asymmetric non-linear vibrations of circular plates with a free edge is presented. The dynamic analogue of the von K" a arm" a an equations is used to establish the governing equations. The plate displacement at a given point is expanded on the linear natural modes. The forcing is harmonic, with a frequency close to the natural frequency o kn of one asymmetric mode of the plate. Thus, the vibration is governed by the two degenerated modes corresponding to o kn ; which are one-to-one internally resonant. An approximate analytical solution, using the method of multiple scales, is presented. Attention is focused on the case where one configuration which is not directly excited by the load gets energy through non-linear coupling with the other configuration. Slight imperfections of the plate are taken into account. Experimental validations are presented in the second part of this paper. #

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“…Provided that modal coupling does not exist and discarding the study of bifurcations [22,23], a one harmonic approach often provides rather accurate backbone curves. In this case, the vector of generalized displacements is written as:…”

Section: The Ordinary Differential Equations Of Motion and Their Solumentioning

confidence: 99%

On displacement based non-local models for non-linear vibrations of thin nano plates

Chuaqui

Ribeiro

2018

MATEC Web Conf.

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Abstract. This paper addresses the formulation of displacement based, non-linear, plate models adopting Eringen's non-local elasticity, to study the modes of vibration of thin, nano plates. Plate models governed by ordinary differential equations of motion with generalized displacements as unknowns have some advantages over mixed type formulations, but difficulties arise in the development of such non-linear models when non-local effects are taken into account. To circumvent those difficulties, approximations of debatable justification can be imposed. Different approximations are discussed here and the accuracy of the best non-local, non-linear displacement based model achieved is put to test, by carrying out comparisons with a model based on Airy's stress function.

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Non-linear free vibration of isotropic plates with internal resonance

Cited by 94 publications

References 14 publications

Identification of cascade of Hammerstein models for the description of nonlinearities in vibrating devices

Identification of cascade of Hammerstein models for the description of nonlinearities in vibrating devices

Asymmetric Non-Linear Forced Vibrations of Free-Edge Circular Plates. Part 1: Theory

On displacement based non-local models for non-linear vibrations of thin nano plates

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